an observer at the top of a 462ft cliff measures the angle of depression from the top of the cliff to a point on the ground to be 5 degrees.

Question

what's the distance from the base of the cliff to the point on the ground? give answer as an exact value in simplest form and as a decimal approximation rounded to the nearest foot.

draw and label a picture of this situation

(HINT: the exact expression is what is entered in the calculator to get the approximate answer)

Answer 1

The observer at the top of a 462 ft cliff measures the angle of depression from the top of the cliff to a point on the ground to be 5°.The angle of depression form the top of the cliff = 5°

The 5° is outside the triangle formed . To find the angle in the triangle we have to subtract 5° from 90°. 90° - 5° = 85° Note sum of an angle on a right angle is 90°.

tan 85° = opposite / adjacent

tan 85° = a / 462

cross multiply

462 × tan 85° = a

a = 11.4300523 × 462

a = 5280.66 ft

the distance is 5281 ft